Week 10
Modelling Uncertainty: Two helpers
Business
The start of the week email. No need to reread it if you received it. It's just linked here in case anyone accidentally deleted it (it's happened before 🥺).
⦿ Monday. Reading break continues ⇒ No classes 😔
⦿ Wednesday. Probabilities from data
Where do probabilities come from? Some probabilities are primarly theoretical, like the chance of getting heads in a toss of a fair coin. But many have their origin in data. Sometimes that data is nicely presented, but when it isn't we need to do some organizing.
- Example: Grade 4 boys' sports participation Pencast 16:19 | PDF
- Some boys play soccer, some play baseball, and some play both. How can we organize the numbers?
- Example: Cancer statistics Pencast 11:02 | PDF
- Smoking, living in urban areas, and having a hazardous occupation are all risk factors for lung cancer. Let's break down the numbers.
Exercises
If you're comfortable with the topics above you're ready to work on:
Supplementary resources:
The only resource I found on the web that focusses just on using set theory for organizing data is this collection of short videos and notes from Ms. Chor at GHCI: Lesson 1: Organized Counting with Venn Diagrams (5.1). If anyone knows of, or finds, something better please share!
⦿ Friday. Essential combinatorics
- For us combinatorics means three things, one principle and two formulas: the Multiplication Principle, and the formulas for Permutations and Combinations.
- The multiplication principle Pencast 9:06| PDF
- For two independent events A and B that can occur in m and n ways respectively, the total number of ways A⋂B can occur is m×n.
- Password combinatorics Pencast 11:19| PDF
- Why you should use long passwords drawn from large sets of characters, and four-digit PIN codes are an abomination.
- Lineups and partial lineups: Permutations Pencast 12:02| PDF
- Permutations count the number of ways r items chosen from n items can be ordered.
- Committees and subsets: Combinations Pencast 7:22| PDF
- Combinations count the number of subsets of r things that can be selected from n things.
- Combinatorics: Formula sheet PDF
- The week's formulas summarized.
- Example: Whitehorse vs "the communities" Pencast 10:09 | PDF
- Is Whitehorse dominating committee memberships? What are the chances that it's a coincidence?
- Example: Playing the lottery Pencast 14:04| PDF
- What are our chances of winning at Lotto Max?
- Example: Eating pizza Pencast 14:31| PDF
- How many Dominos pizzas are possible?
Exercises
If you're comfortable with the topics above you're ready to work on:
Supplementary resources:
§3.5 in Chapter 3 of College Mathematics for Everyday life by Inigo, Jameson, Kozak, Lanzetta, and Sonier covers combinatorics.
Assignment
Assignment 10 is posted. Due by 1 pm Friday March 27. Note that the problems are worth different numbers of marks. Use your time wisely.
- You can hand in work done by hand to me in class or in dropbox A19.
- Excel or other binary files should be sent as file attachments to an email message.
- Google sheets can be submitted by sharing a link to them.
- Work done in Desmos can be submitted by sharing a link to your saved graph.
Name the file you submit A10_firstname.pdf, e.g.
A10_Tim.pdf
If you have to submit multiple files, add a suffix number to each, e.g.
A10_Tim_1.pdf
A10_Tim_2.pdf